Problem: Simplify the following expression: $k = \dfrac{-50t - 50}{-90t - 100}$ You can assume $t \neq 0$.
Explanation: Find the greatest common factor of the numerator and denominator. The numerator can be factored: $-50t - 50 = - (2\cdot5\cdot5 \cdot t) - (2\cdot5\cdot5)$ The denominator can be factored: $-90t - 100 = - (2\cdot3\cdot3\cdot5 \cdot t) - (2\cdot2\cdot5\cdot5)$ The greatest common factor of all the terms is $10$ Factoring out $10$ gives us: $k = \dfrac{(10)(-5t - 5)}{(10)(-9t - 10)}$ Dividing both the numerator and denominator by $10$ gives: $k = \dfrac{-5t - 5}{-9t - 10}$